I am trying to alter the 4 points of the polygon so that it changes into a different shape, size, and location. In the following code, all of the animations work perfectly except for the last one that deals with the points. I have tried to use PointAnimation instead of DoubleAnimation but it still throws an error when loading the silverlight object.

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Animating points is a bit verbose with Silverlight. You do need to use a PointAnimation, but can only animate one point per animation. To do this, you'll probably need to go to a Path, like the snippet below (add your transform, fill, and stroke just like the polygon). You then create a series of PointAnimations, each targetting a point, so you'll need four animations to move the four points. If you are going to be doing a lot of this, you may want to try and get some of this functionality into a user or custom control.